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Uspekhi Mat. Nauk, 1983, Volume 38, Issue 1(229), Pages 3–67 (Mi umn2823)  

This article is cited in 124 scientific papers (total in 124 papers)

Integrability and non-integrability in Hamiltonian mechanics

V. V. Kozlov

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English version:
Russian Mathematical Surveys, 1983, 38:1, 1–76

Bibliographic databases:

UDC: 517.911
MSC: 70H06, 70H07, 70H08, 37J30, 74H60
Received: 25.05.1982

Citation: V. V. Kozlov, “Integrability and non-integrability in Hamiltonian mechanics”, Uspekhi Mat. Nauk, 38:1(229) (1983), 3–67; Russian Math. Surveys, 38:1 (1983), 1–76

Citation in format AMSBIB
\by V.~V.~Kozlov
\paper Integrability and non-integrability in Hamiltonian mechanics
\jour Uspekhi Mat. Nauk
\yr 1983
\vol 38
\issue 1(229)
\pages 3--67
\jour Russian Math. Surveys
\yr 1983
\vol 38
\issue 1
\pages 1--76

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    1. V. V. Trofimov, A. T. Fomenko, “Liouville integrability of Hamiltonian systems on Lie algebras”, Russian Math. Surveys, 39:2 (1984), 1–67  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. V. Kozlov, “Calculus of variations in the large and classical mechanics”, Russian Math. Surveys, 40:2 (1985), 37–71  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. T. C. Bountis, V. Papageorgiou, P. Winternitz, “On the integrability of systems of nonlinear ordinary differential equations with superposition principles”, J Math Phys (N Y ), 27:5 (1986), 1215  crossref  mathscinet  zmath  adsnasa  isi
    4. A. T. Fomenko, “The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability”, Math. USSR-Izv., 29:3 (1987), 629–658  mathnet  crossref  mathscinet  zmath
    5. V. V. Kozlov, “The splitting of separatrices and the generation of isolated periodic solutions in Hamiltonian systems with one-and-a-half degrees of freedom”, Russian Math. Surveys, 41:5 (1986), 149–150  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Haruo Yoshida, “Existence of exponentially unstable periodic solutions and the non-integrability of homogeneous Hamiltonian systems”, Physica D: Nonlinear Phenomena, 21:1 (1986), 163  crossref
    7. I. A. Taimanov, “Topological obstructions to integrability of geodesic flows on non-simply-connected manifolds”, Math. USSR-Izv., 30:2 (1988), 403–409  mathnet  crossref  mathscinet  zmath  isi
    8. S. L. Ziglin, “Splitting of the separatrices and the nonexistence of first integrals in systems of differential equations of Hamiltonian type with two degrees of freedom”, Math. USSR-Izv., 31:2 (1988), 407–421  mathnet  crossref  mathscinet  zmath
    9. Jarmo Hietarinta, “Direct methods for the search of the second invariant”, Physics Reports, 147:2 (1987), 87  crossref
    10. Emil Horozov, “On the non-integrability of Gross-Neveu models”, Annals of Physics, 174:2 (1987), 430  crossref
    11. Tassos Bountis, V. Papageorgiou, M. Bier, “On the singularity analysis of intersecting separatrices in near-integrable dynamical systems”, Physica D: Nonlinear Phenomena, 24:1-3 (1987), 292  crossref
    12. Jair Koiller, J.M. Balthazar, T. Yokoyama, “Relaxation-chaos phenomena in celestial mechanics”, Physica D: Nonlinear Phenomena, 26:1-3 (1987), 85  crossref
    13. Haruo Yoshida, “A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential”, Physica D: Nonlinear Phenomena, 29:1-2 (1987), 128  crossref
    14. Hioe F.T., “Hamiltonian systems with a certain stability property”, J. Phys. A, 21:7 (1988), L377–L380  crossref  zmath  adsnasa  isi
    15. A. T. Fomenko, H. Zieschang, “On typical topological properties of integrable Hamiltonian systems”, Math. USSR-Izv., 32:2 (1989), 385–412  mathnet  crossref  mathscinet  zmath
    16. V. V. Kozlov, D. V. Treschev, “On the integrability of Hamiltonian systems with toral position space”, Math. USSR-Sb., 63:1 (1989), 121–139  mathnet  crossref  mathscinet  zmath
    17. Richard C Churchill, David L Rod, “Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems”, Journal of Differential Equations, 76:1 (1988), 91  crossref
    18. Koiller J., Carvalho S.P., “Non-integrability of the 4-vortex system: analytical proof”, Comm. Math. Phys., 120:4 (1989), 643–652  crossref  mathscinet  zmath  isi
    19. F. T. Hioe, “Certain stability type and integrable two-dimensional Hamiltonian systems”, Phys Rev A, 39:5 (1989), 2628  crossref  mathscinet  adsnasa  isi
    20. V. G. Papageorgiou, M. L. Glasser, T. C. Bountis, “Mel’nikov’s Function for Two-Dimensional Mappings”, SIAM J Appl Math, 49:3 (1989), 692  crossref  mathscinet  zmath  isi
    21. D. V. Treschev, “The mechanism of destruction of resonance tori of Hamiltonian systems”, Math. USSR-Sb., 68:1 (1991), 181–203  mathnet  crossref  mathscinet  zmath  isi
    22. A. T. Fomenko, “The symplectic topology of completely integrable Hamiltonian systems”, Russian Math. Surveys, 44:1 (1989), 181–219  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. A. Ramani, B. Grammaticos, T. Bountis, “The Painlevé property and singularity analysis of integrable and non-integrable systems”, Physics Reports, 180:3 (1989), 159  crossref
    24. K M Tamizhmani, A Annamalai, J Phys A Math Gen, 23:13 (1990), 2835  crossref  mathscinet  zmath  adsnasa  isi
    25. A. T. Fomenko, H. Zieschang, “A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom”, Math. USSR-Izv., 36:3 (1991), 567–596  mathnet  crossref  mathscinet  zmath  adsnasa
    26. A. V. Bolsinov, S. V. Matveev, A. T. Fomenko, “Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity”, Russian Math. Surveys, 45:2 (1990), 59–94  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    27. I. V. Krivoshei, “Instability criterion for multidimensional nonlinear Hamiltonian systems”, Theoret. and Math. Phys., 82:2 (1990), 187–194  mathnet  crossref  mathscinet  zmath  isi
    28. Zhuhan Jiang, S. Rauch-Wojciechowski, “Integrable dynamical systems with quadratic and cubic nonlinearities related to graded Lie algebras”, J Math Phys (N Y ), 32:7 (1991), 1720  crossref  mathscinet  zmath  isi
    29. S. Ichtiaroglou, G. Voyatzis, E. Meletlidou, “Conditions for the existence of periodic solutions to integrable two-dimensional Hamiltonian systems”, Phys Rev A, 43:12 (1991), 7043  crossref  adsnasa  isi
    30. A. T. Fomenko, “A bordism theory for integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of higher-dimensional integrable systems”, Math. USSR-Izv., 39:1 (1992), 731–759  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    31. Gabriel P. Paternain, “On the topology of manifolds with completely integrable geodesic flows”, Ergod Th Dynam Sys, 12:1 (1992)  crossref  mathscinet
    32. Maorong Zou, “Monodromy in two degrees of freedom integrable systems”, Journal of Geometry and Physics, 10:1 (1992), 37  crossref
    33. Paternain G.P., “Real analytic convex surfaces with positive topological entropy and rigid body dynamics”, Manuscripta Math., 78:1 (1993), 397–402  crossref  mathscinet  zmath  isi
    34. M. Lakshmanan, R. Sahadevan, “Painlevé analysis, Lie symmetries, and integrability of coupled nonlinear oscillators of polynomial type”, Physics Reports, 224:1-2 (1993), 1  crossref
    35. Bialy M., “Polynomial integrals for a Hamiltonian system and breakdown of smooth solutions for quasi-linear equations”, Nonlinearity, 7:4 (1994), 1169–1174  crossref  mathscinet  zmath  adsnasa  isi  elib
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    39. Gabriel P. Paternain, “On the topology of manifolds with completely integrable geodesic flows II”, Journal of Geometry and Physics, 13:3 (1994), 289  crossref
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    41. Keith Burns, Howard Weiss, “A geometric criterion for positive topological entropy”, Comm Math Phys, 172:1 (1995), 95  crossref  mathscinet  zmath  adsnasa  isi
    42. V Azriel, “A hard-sphere model for the reactions of two diatomic molecules with ionic bond”, Chemical Physics, 199:2-3 (1995), 195  crossref  elib
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    60. Andrzej J. Maciejewski, Sasho Ivanov Popov, Jean-Marie Strelcyn, “The Euler equations on Lie algebra so(4): An elementary approach to integrability condition”, J Math Phys (N Y ), 42:6 (2001), 2701  crossref  mathscinet  zmath  isi
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    64. Page D.N., Kubizňák D., Vasudevan M., Krtouš P., “Complete integrability of geodesic motion in general higher-dimensional rotating black-hole spacetimes”, Phys. Rev. Lett., 98:6 (2007), 061102 \totalapges 4  crossref  mathscinet  isi
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    67. Long, YM, “Collection of problems proposed at International Conference on Variational Methods”, Frontiers of Mathematics in China, 3:2 (2008), 259  crossref  mathscinet  zmath  isi
    68. Okulov V.L., “Chaotic advection and separatrix branching in the Lagrangian diagnostics of flows”, Dokl. Phys., 54:3 (2009), 134–139  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    70. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Russian Math. Surveys, 65:2 (2010), 259–318  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    105. M. V. Shamolin, “Integrable systems on the tangent bundle of a multi-dimensional sphere”, J. Math. Sci. (N. Y.), 234:4 (2018), 548–590  mathnet  crossref
    106. Bolsinov A., “Singularities of Bi-Hamiltonian Systems and Stability Analysis”: Bolsinov, A MoralesRuiz, JJ Zung, NT, Geometry and Dynamics of Integrable Systems, Adv. Courses Math CRM Barc., Advanced Courses in Mathematics Crm Barcelona, Birkhauser Verlag Ag, 2016, 35–84  crossref  isi
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    117. Shamolin V M., “New Cases of Integrable Odd-Order Systems With Dissipation”, Dokl. Math., 101:2 (2020), 158–164  crossref  isi
    118. Shamolin V M., “New Cases of Homogeneous Integrable Systems With Dissipation on Tangent Bundles of Two-Dimensional Manifolds”, Dokl. Math., 102:2 (2020), 443–448  crossref  isi
    119. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem devyatogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 68–81  mathnet  crossref
    120. M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118  mathnet  crossref
    121. M. V. Shamolin, “Predelnye mnozhestva differentsialnykh uravnenii okolo singulyarnykh osobykh tochek”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 119–128  mathnet  crossref
    122. I. A. Bizyaev, I. S. Mamaev, “Dinamika pary tochechnykh vikhrei i profilya s parametricheskim vozbuzhdeniem v idealnoi zhidkosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 618–627  mathnet  crossref
    123. A. A. Kilin, E. N. Pivovarova, “Neintegriruemost zadachi o kachenii sfericheskogo volchka po vibriruyuschei ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 628–644  mathnet  crossref
    124. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei”, Materialy mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu v prikladnykh naukakh “International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19”. Belgorod, 20–24 avgusta 2019 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 195, VINITI RAN, M., 2021, 142–156  mathnet  crossref
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